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标题: Derivatives【 Reading 38】习题精选 [打印本页]
作者: optiix    时间: 2012-4-2 14:38     标题: [2012 L3] Derivatives【Session15- Reading 38】习题精选

Which of the following positions results in synthetic fixed-rate debt?
A)
A long position in a floating-rate note combined with a pay-fixed interest rate swap.
B)
A short position in a floating-rate note combined with a pay-fixed interest rate swap.
C)
A long position in a floating-rate note combined with a receive-fixed interest rate swap.


The receive-floating part of the interest rate swap offsets the floating rate payments the short-bond position requires. Therefore, a synthetic fixed-rate debt position is created.
作者: optiix    时间: 2012-4-2 14:43

A borrower with a $4 million floating rate loan pays LIBOR plus 200 basis points on the loan. Payments are semiannual. The borrower wishes to convert this obligation to a fixed-rate loan. The borrower uses a swap with a fixed rate equal to 5.6%, floating rate equal to LIBOR, and notional principal equal to $4 million. Which of the following most closely approximates the semiannual payments made by the borrower on the loan and the swap?
A)
$76,000.
B)
$72,000.
C)
$152,000.


The borrower will enter into the swap to receive LIBOR and pay 5.6%. The LIBOR payment effectively passes from the counterparty through to the lender while the 200 basis point spread remains an obligation of the borrower. Thus, the borrower pays (0.056 + 0.02) / 2 on $4 million each six months = $152,000.
作者: optiix    时间: 2012-4-2 14:45

Which of the following statements about debt is least accurate?
A)
To create synthetic dual currency debt, the portfolio manager can issue domestic debt and enter into a fixed-for-fixed currency swap where notional principal is swapped at origination.
B)
To create synthetic callable debt from existing noncallable debt, the portfolio manager can enter into a receiver's swaption.
C)
The all-in-cost is another way of saying "the internal rate of return of a financing alternative."


To create synthetic dual currency debt, the portfolio manager can issue domestic debt and enter into a fixed-for-fixed currency swap where notional principal is NOT swapped at origination.
作者: optiix    时间: 2012-4-2 14:46

To create synthetic fixed-rate debt from a floating-rate obligation, a portfolio manager can do which of the following?
A)
Pay variable and receive fixed in a swap.
B)
Sell interest rate caps.
C)
Pay fixed and receive variable in a swap.


To create synthetic fixed-rate debt, a portfolio manager can pay fixed and receive variable in a swap.
作者: optiix    时间: 2012-4-2 14:46

A firm has most of its liabilities in the form of floating-rate notes with a maturity of two years and quarterly reset. The firm is concerned with interest rate movements over the next eight quarters but is not concerned with potential movements after that. Which of the following strategies will allow the firm to hedge the expected change in interest rates?
A)
Enter into a 2-year, quarterly pay-floating, receive-fixed swap.
B)
Enter into a 2-year, quarterly pay-fixed, receive-floating swap.
C)
Buy a swaption that allows the firm to be the fixed-rate payer upon exercise. In other words, go long a payer’s swaption with a 2-year maturity.


The firm should receive floating to offset the floating-rate obligation. Given its goals, the firm should enter into the swap to hedge the immediate risk and not the future risk offered by the swaption.
作者: optiix    时间: 2012-4-2 14:47

Jane Hiatt and Penny Hoskins have responsibility for interest rate and currency risk management for the Rensselaer Corporation, a large multinational firm based in the Midwestern United States.
Due to an increase in global economic growth, Rensselaer has seen its sales increase and is planning to expand its U.S. factory at a cost of $30,000,000. The factory expansion will be financed at a floating interest rate of LIBOR plus 200 basis points, with payments made quarterly over seven years. Hiatt expects that Rensselaer will begin the expansion in six months and will receive the $30,000,000 in financing at that point in time. She is concerned, however, that global interest rates will increase in the interim and would like to have the option to convert the loan’s interest rate to a fixed rate in six months. Hiatt evaluates the forecasts for future swap fixed rates as well as the current terms of various swaptions, provided in the following table. The swaptions are for a 7-year swap where the floating interest rate is LIBOR flat.

Fixed rate for payer's swaption that matures in six months

7.00%


Fixed rate for receiver's swaption that matures in six months

7.10%


Projected Swap Fixed Rate in six months

7.20%


Fixed rate for payer's swaption that matures in seven years

8.40%


Fixed rate for receiver's swaption that matures in seven years

8.50%


Projected Swap Fixed Rate in seven years

9.20%


Rensselaer has just opened a factory in Germany that will sell products locally, earning projected cash flows of €10,000,000 on a quarterly basis. In order to convert these cash flows into dollars, Hoskins suggests that Rensselaer enter into a currency swap without an exchange of notional principal where euros will be exchanged for dollars. Hoskins contacts a currency swap dealer and reports the following exchange rate and annual swap fixed interest rates. These rates are for an exchange of cash flows starting in three months, which is approximately when Rensselaer will receive its next euro cash flow from its German operation. The maturity of the swap will be two years, because Hoskins does not feel comfortable projecting cash flows from the German factory beyond the next two years.

Exchange rate (EUR per dollar)

0.72


Swap interest rate in U.S. dollars

3.40%


Swap interest rate in euros

5.80%

Given her interest rate forecasts, which of the following is the most likely position Hiatt should recommend Rensselaer take to hedge the financing of the factory expansion?
A)
Buy a seven year maturity payer swaption.
B)
Buy a six month maturity payer swaption.
C)
Buy a six month maturity receiver swaption.


If LIBOR increases as she expects, the cost of Rensselaer’s floating rate loan will increase. In this case the firm will want to pay a fixed rate and receive a floating rate in a swap. The payer’s swaption will allow them to pay a predetermined fixed rate in a swap. The maturity of the swaption should coincide with the initiation of the loan. (Study Session 15, LOS 38.h)
Assume the firm buys the appropriate swaption and Hiatt’s interest rate forecasts prove correct. Determine which of the following is closest to the net interest payment Rensselaer will make on the factory expansion loan in six months.
A)
$675,000.
B)
$682,500.
C)
$690,000.

If interest rates increase and the fixed rate on swaps in six months (projected at 7.2%) exceeds the swaption fixed rate, the firm will exercise the swaption and pay 7.0%. They receive LIBOR from the swap in the swaption and pay in total 7.0% + 2.0% = 9% in the swap and the loan. The firm’s first quarterly payment in net will be 9% × $30,000,000 × 90/360 = $675,000.
Note that if swap fixed rates are less than 7.0% in six months, the firm would not exercise the swaption. The firm could either a) enter a swap at that time and pay the lower fixed rate or b) not enter a swap and just pay the floating rate in the loan. (Study Session 15, LOS 38.h)
If Hiatt’s interest rate forecasts prove correct, and the appropriate hedge is enacted, which of the following best represents the changes in Rensselaer’s risk exposure? The firm’s cash flow risk:
A)
decreases and its market value risk decreases.
B)
decreases and its market value risk increases.
C)
increases and its market value risk decreases.

A floating-rate cash flow will have a very low duration which means that its market value is largely resistant to changing interest rates. If Rensselaer hedges its floating rate loan so that it becomes a synthetic fixed rate loan, they have increased its duration and increased its sensitivity to changes in interest rates. So the loan’s market value risk increases.
However, they will have decreased the sensitivity of the cash flows in the loan to changes in interest rates, so cash flow risk declines. (Study Session 15, LOS 38.c)
What are the periodic cash flows resulting from Rensselaer’s hedge of the German factory sales?
A)
$4,264,706.
B)
$8,141,762.
C)
$13,888,889.

In order to calculate how much Rensselaer will receive in dollars as a result of the swap, first calculate the implied notional principal (NP) from the quarterly cash flows of EUR 10,000,000, using the quarterly euro interest rate:
Next, calculate the dollar implied principal at the current exchange rate: EUR 689,655,172.41/0.72 = $957,854,406.13. Lastly, calculate a dollar cash flow using the quarterly dollar interest rate:
$957,854,406.13 × 0.034/4 = $8,141,762. (Study Session 15, LOS 38.f)
Suppose that Rensselaer’s currency swap can be structured with fixed or floating payments. If Hiatt’s interest rate concerns are correct, which of the following would be the ideal position for Rensselaer to take in the currency swap? From Rensselaer’s perspective, the swap should be structured with a:
A)
fixed dollar interest rate and a floating euro interest rate.
B)
floating dollar interest rate and a fixed euro interest rate.
C)
floating dollar interest rate and a floating euro interest rate.


Hiatt is concerned that global interest rates will increase. In the currency swap, Rensselaer will pay euros and receive dollars. They will therefore want to fix the euro interest rate and receive dollars at a floating interest rate, which is expected to be higher in the future. (Study Session 15, LOS 38.a)
In the currency swap, Rensselaer is exposed to:
A)
credit risk and economic risk.
B)
credit risk.
C)
neither credit risk nor economic risk.


Rensselaer has credit risk because if the swap counterparty defaults on the contract, Rensselaer will not have hedged its dollar cash flows. Rensselaer is also exposed to the type of currency risk referred to as economic risk to the extent that local asset and currency movements are correlated. Economic risk refers to longer term noncontractual exchange rate risk and the amount to hedge is not readily determined. Hoskins states that she does not feel comfortable projecting cash flows from the German factory beyond the next two years. She therefore is uncertain how much to hedge in the future and Rensselaer has economic risk. (Study Session 15, LOS 38.a)
作者: optiix    时间: 2012-4-2 14:48

For a plain-vanilla interest-rate swap with annual reset and one year to maturity, which of the following is closed to the duration for the floating side of the swap?
A)
0.50.
B)
1.00.
C)
0.75.


The duration of the floating side is 1/2 the time until the next reset date. Since this is an annual pay swap with 1 year left the duration of the floating side is 1 x .5 = .5 or 1 divided by 2 = .5. The duration of the fixed side of a swap is approximately .75 to the time until maturity. If we take a different example of a 4 year swap with semi-annual payments the duration of the fixed side would be .75 x 4 = 3 and the duration of the floating side is .5 / 2 = .25.
作者: optiix    时间: 2012-4-2 14:48

For a pay-fixed counterparty, the duration of the swap will generally be (in absolute value terms):
A)
greater than the duration of the fixed-rate payments.
B)
less than the duration of the fixed-rate payments.
C)
equal to the duration of the fixed-rate payments.


Since the problem asks only about the absolute value, we can ignore the fact that the duration for this position will be opposite in sign to that we usually calculate. Although most of the duration is associated with the fixed payments, the next “floating” payment is predetermined. Therefore, for example, the duration of a quarterly-reset swap might be duration of fixed payments minus 0.25. Because she receives floating-rate cash flows, taking the pay–fixed/receive–floating position in a swap decreases the dollar duration of a fixed income portfolio.
作者: optiix    时间: 2012-4-2 14:49

The duration of a pay-floating swap is obtained by:
A)
adding the duration of the floating-rate payments to the duration of the fixed-rate payments.
B)
dividing the duration of the floating-rate payments by the duration of the fixed-rate payments.
C)
subtracting the duration of the floating-rate payments from the duration of the fixed-rate payments.


The duration of a pay-floating swap is the difference between the duration of the payments. Expressed as the formula: DPay-floating = DFixed-rate payments – DFloating-rate payments.
作者: optiix    时间: 2012-4-2 14:50

Which of the following positions results in synthetically issuing floating-rate debt?
A)
A long position in a fixed-rate bond combined with a receive-fixed interest rate swap.
B)
A short position in a fixed-rate bond combined with a receive-fixed interest rate swap.
C)
A long position in a fixed-rate bond combined with a pay-fixed interest rate swap.


The receive-fixed part of the interest rate swap offsets the fixed rate payments the short bond position requires. Therefore, a synthetic floating-rate debt position is created.
作者: optiix    时间: 2012-4-2 14:50

Which of the following statements regarding a firm that currently has fixed-rate, noncallable domestic debt outstanding is least accurate? The firm:
A)
can turn the debt into floating rate by entering a receive-fixed swap position.
B)
can turn the debt into callable debt by entering into a receiver's swaption position.
C)
is exposed to an increase in interest rates.


The firm isn’t concerned with rising rates. If rates fall, however, they face an increase in the value of their liabilities or market value risk (which is a type of interest rate risk).
作者: optiix    时间: 2012-4-2 14:51

A pay-floating counterparty in a plain-vanilla interest-rate swap also holds a long position in a fixed-rate bond. If the maturity of the bond and swap are both two years, the duration of the position will be:
A)
greater than the duration of the bond alone.
B)
zero.
C)
less than the duration of the bond but greater than zero.


The duration of the position will increase with the addition of the pay-floating/receive-fixed position. Both of the remaining answers cannot be correct.
作者: optiix    时间: 2012-4-2 14:51

Which of the following statements is most accurate? The duration of a long-position in a floating-rate note is:
A)
close to zero and is unaffected by the addition of a receive-floating position in a swap.
B)
close to zero but increases with the addition of a pay-floating position in a swap.
C)
equal to its maturity but decreases to near zero with the addition of a pay-floating position in a swap.


A floating-rate note’s value will be relatively stable because the payments vary with changes in the interest rates. For the long position (the lender), adding a pay-floating position will produce a synthetic fixed-rate position whose value will change with changes in interest rates.
作者: optiix    时间: 2012-4-2 14:52

A firm has outstanding floating rate debt on which they pay LIBOR + 200 basis points, and management expects interest rates to increase in the very near future. In order to create synthetic fixed-rate debt, the best strategy for the firm is to enter into a swap in which they:
A)
receive floating and pay floating.
B)
pay fixed and receive floating.
C)
pay floating and receive fixed.


To create synthetic fixed-rate debt, the firm should pay fixed and receive floating in a swap. The floating rate payment they receive in the swap will partially offset the floating rate they pay on their debt. Any portion of the floating rate on the debt that remains (assume 100bps) will add to the fixed rate they pay on the swap. Their net position on the debt and the swap will be pay fixed + 100 bps = fixed rate.
作者: optiix    时间: 2012-4-2 14:53

For an issuer of a floating-rate note, the market value of the loan will be:
A)
volatile, but the position will become more stable with the addition of a receive-floating swap position.
B)
zero with the addition of a pay-floating swap position.
C)
relatively stable but the position will become less stable with the addition of a receive-floating swap position.


A floating-rate note’s value will be relatively stable because the payments vary with changes in the interest rates. Adding a receive-floating position will produce a synthetic fixed-payment position whose value will change with changes in interest rates.
作者: optiix    时间: 2012-4-2 14:53

A manager of a $2 million dollar fixed-income portfolio with a duration of 3 wants to increase the duration to 4. The manager chooses a swap with a net duration of 2. The manager should become a:
A)
pay-floating counterparty in the swap with a notional principal of $1 million.
B)
pay-floating counterparty in the swap with a notional principal of $2 million.
C)
receive-floating counterparty in the swap with a notional principal of $1 million.


To increase duration, the manager should be a pay-floating/receive-fixed counterparty in the swap with a notional principal equal to:
NP = $2,000,000 × (4 − 3) / 2
NP = $1,000,000.
作者: optiix    时间: 2012-4-2 14:54

A manager of a $40 million dollar fixed-income portfolio with a duration of 4.2 wants to lower the duration to 3. The manager chooses a swap with a net duration of 2.1. What notional principal (NP) should the manager choose for the swap to achieve the target duration?
A)
$22,857,143.
B)
$56,000,000.
C)
$70,000,000.


NP = $40,000,000 × (3 − 4.2) / -2.1NP = $22,857,143
Since the manager wants to reduce the duration of his portfolio, he should take a receive-floating/pay-fixed position in the swap with that notional principal. Remember that a receive-floating swap has a negative duration, so we enter –2.1 in the equation.
作者: optiix    时间: 2012-4-2 14:54

If a fixed-income portfolio manager wants to double the duration of a portfolio with a swap that has the same duration as the portfolio, then the notional principal would be:
A)
half the value of the portfolio.
B)
twice the value of the portfolio.
C)
equal to the value of the portfolio.


The number of contracts to change the DD of a portfolio is the (DTarget – Dcurrent)/DD of instrument used

Since we use only one contract with swaps, we set the number of contracts equal to 1.0:

1 = (DDTarget – DDcurrent)/DDswap

Then convert dollar duration, DD, into value times duration, D:

1 = [DTarget(VP) – Dcurrent(VP)] / DS(NP) → (VP) (DTarget – Dcurrent) / DS(NP)

If we then rearrange the equation by moving NP to the other side we get…

NP = (VP)(DTarget – Dcurrent) / DS

With the target duration = 2 X current portfolio duration with the swap having the same duration as the current portfolio we then have
NP = (VP)(2DTarget – Dcurrent) / DS NP = (VP)(D) / D
NP = VP
作者: optiix    时间: 2012-4-2 14:55

From the borrower’s perspective, a plain-vanilla currency swap can create a synthetic fixed-rate euro loan when entered into as a:
A)
fixed-rate receiver and combined with a fixed-rate dollar loan.
B)
floating-rate receiver and combined with a floating-rate dollar loan.
C)
floating-rate receiver and combined with a fixed-rate dollar loan.


The borrower has borrowed dollars and pays a floating rate. Becoming the floating-rate receiver in the swap will mean swapping the dollars and getting the floating-rate payments on the dollars to pass through to the original lender. The borrower will then pay fixed on the euros received.
作者: optiix    时间: 2012-4-2 14:56

A European firm can borrow at 8% in the U.S. and at 7% in Europe. A U.S. firm can borrow at 7% in the U.S. and at 8% in Europe. If the U.S. firm needs euros and the European firm needs dollars, then a currency swap could save each counterparty:
A)
a minimum of 2% a loan on the foreign currency.
B)
up to 1% (maximum) in a loan on the foreign currency.
C)
a minimum of 1% in a loan on the foreign currency.


The European firm can borrow euros at 7% and lend them at that rate to the U.S. firm who then saves 1%. The American firm, in turn, can borrow dollars at 7% and lend them at that rate to the European firm who then also saves 1%. It could also be possible for the American firm to re-lend the dollars at, say 7.5%, and still get the Euros at a lower rate, say 7.1%. Such an arrangement would mean the net rate on the loan is less than 7% for the American firm and more than 7% for the European firm. Such a discrepancy is unlikely, however, and the 1% (maximum) savings each is the only possible answer.
作者: optiix    时间: 2012-4-2 14:56

A U.S. firm that wishes to convert its annual cash flows of €20 million each to dollars upon receipt. The exchange rate is currently €0.9/USD, and the swap rates in the U.S. and Europe are both 6.1 percent. Appropriately using a fixed-for-fixed currency swap that does not exchange principal, what would be the annual dollar cash flow to the firm?
A)
$32,786,885.
B)
$10,980,000.
C)
$22,222,222.


At current interest rates, the €20 million per year translates to a notional principal of:
NP = 20,000,000 / 0.061
NP = €327,868,852
The corresponding dollar amount is $364,298,725 = €327,868,852 / (€0.9/$). The annual interest payments on this amount would be $22,222,222 = $364,298,725 × 0.061.
作者: optiix    时间: 2012-4-2 14:56

A U.S. firm that wishes to convert its quarterly cash flows of €7 million each to dollars upon receipt. The exchange rate is currently €0.8/US$, and the swap rates in the U.S. and Europe are 5.2 percent and 5.6 percent respectively. What should be the notional principal of a currency swap, where the principal is not exchanged and the rates are fixed, that will accomplish the goal?
A)
$625,000,000.
B)
€500,000,000.
C)
$8,125,000.


At current interest rates, the €7 million per quarter translates to a notional principal in the foreign currency of:
NP = 7,000,000 / (0.056 /4)
NP = €500,000,000

The notional principal in U.S. dollar terms is: €500,000,000 X US$/ €0.8 = $625,000,000
The quarterly cash flows on the swap would then be $625,000,000 X 0.52/4 = $8,125,000
作者: optiix    时间: 2012-4-2 14:57

A U.S. firm that wishes to convert its annual cash flows of €10 million each to US$ upon receipt. The exchange rate is currently 0.9€/$, and the swap rates in the U.S. and Europe are 5.4% and 5% respectively. Appropriately using a fixed-for-fixed currency swap that does not exchange principal, what would be the annual dollar cash flow to the firm?
A)
$22,222,222.
B)
$11,111,111.
C)
$12,000,000.


At current interest rates, the €10 million per year translates to a notional principal of:
NP = 10,000,000 / 0.05
NP = €200,000,000
The corresponding dollar amount is $222,222,222 = €200,000,000 / (0.9€/$). The annual interest payments on this amount would be $12,000,000 = $222,222,222 × 0.054.
作者: optiix    时间: 2012-4-2 14:57

A manager of a $300 million bond portfolio consisting of $50 million in investment-grade corporate bonds and $250 million in U.S. Treasuries wants to re-weight to a 50/50 mix. This can be done with a bond-index swap with a notional principal of:
A)
$100 million.
B)
$275 million.
C)
$250 million.


The swap would exchange the return on $100 million in U.S. Treasuries for the return on $100 million of the corporate bonds. This would create a synthetic mix of $150 million in each position.
作者: jawz    时间: 2012-4-2 14:58

An investor who enters into a swap to exchange half the return on her 100,000 share position in a stock for the return on an equal value of the S&P 500 would most likely be trying to:
A)
reduce systematic risk in the portfolio.
B)
diversify her portfolio.
C)
increase the risk and return of her position.


Entering into a swap to exchange the returns on the stock for those of the index would be way to create synthetic diversification in a portfolio. Note that the added diversification as a result of the swap would reduce unsystematic risk, but systematic risk will still exist.
作者: jawz    时间: 2012-4-2 14:58

An investor has a $5,000,000 investment in small-cap stocks. The investor enters into an equity index swap where the investor pays the return on the Russell 2000 and receives the return on the Dow Jones Industrial Average. The notional principal of the swap is $1 million. The resulting position is a synthetic mix of:
A)
16.67% large stocks and 83.33% small stocks.
B)
20% large stocks and 80% small stocks.
C)
25% large stocks and 75% small stocks.


After the swap, $1 million, or 20% of the portfolio’s exposure will be invested in the Dow Jones Industrial Average index of large stocks. $4 million, or 80% of the portfolio will remain invested in small stocks. The $1 million notional principal represents 20% of the position. That is the amount that has been synthetically transferred from one class of assets to the other.
作者: jawz    时间: 2012-4-2 14:59

A borrower who is also the owner of a swaption that gives the holder the right to become a fixed-rate payer and floating-rate receiver would most likely do which of the following? Exercise the swaption when interest rates:
A)
increase to convert a fixed-rate loan to a floating-rate loan.
B)
increase to convert a floating-rate loan to a fixed-rate loan.
C)
decrease to convert a floating-rate loan to a fixed-rate loan.


The owner will benefit when interest rates increase because the owner has the right to pay a fixed rate and receive the floating rate, which will be higher with the increase in interest rates. Receiving the floating rate and paying the fixed rate can turn a floating-rate loan to a fixed-rate loan.
作者: jawz    时间: 2012-4-2 15:00

A firm contracts to borrow $5 million in one year. The firm enters into a one-year swaption where the swap maturity and notional principal match that of the planned loan. The swaption gives the firm the right to be a floating-rate payer. This hedging strategy would be most effective if the loan contract specifies a:
A)
variable rate and interest rates decline.
B)
variable rate and interest rates increase.
C)
fixed rate and interest rates decline.


A firm that has contracted to borrow at a fixed rate in the future would want a hedge against interest rates falling and being stuck paying a higher-than-market rate. A swaption to become a floating-rate payer benefits the owner when interest rates decline. The firm will receive a “high” fixed rate and pay “low” variable rates, and this will offset the higher-than-market rate in the contract.
作者: jawz    时间: 2012-4-2 15:00

A firm has most of its liabilities in the form of floating-rate notes with a maturity of two years and a quarterly reset. The firm is not concerned with interest rate movements over the next four quarters but is concerned with potential movements after that. Which of the following strategies will allow the firm to hedge the expected change in interest rates?
A)
Go long a payer’s swaption with a 1-year maturity.
B)
Enter into a 2-year, quarterly pay-fixed, receive-floating swap.
C)
Go short a payer’s swaption with a 2-year maturity.


The firm will want to receive floating payments to offset the volatility of its floating-rate obligations. A payer’s swaption allows the firm to become a fixed-rate payer/floating-rate receiver in a swap. The one-year maturity corresponds to the start of the period of concern.



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